Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t... Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white...This is a thought-provoking essay, best read in toto at the New York Times.
California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take...
Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job... Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job...
Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic. But a definitive analysis by the Georgetown Center on Education and the Workforce forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above...
Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status...
Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives.
03 August 2012
"In real life there is no such thing as algebra"
That quote, attributed to humorist Fran Lebowitz, will serve as a good title for these excerpts from a recent New York Times op/ed piece that asks "Is Algebra Necessary?"
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I've used basic algebra countless times in real life to quickly solve problems while people next to me slogged through basic mathematics at a much slower pace.
ReplyDeleteI recommend anyone who reads this article also check out some of the counters to it:
http://www.huffingtonpost.com/david-h-bailey/algebra-is-essential-in-a_b_1724338.html
http://blogs.scientificamerican.com/observations/2012/07/30/abandoning-algebra-is-not-the-answer/
http://www.patheos.com/blogs/friendlyatheist/2012/07/31/why-algebra-is-necessary-rebutting-andrew-hacker/
Oh, yes! But I fear the automation in our lives has also made the average human incapable of basic math!
DeleteHow many of us have tried to give a cashier an extra one dollar bill and some change in order to get back a five dollar bill - only to have the cashier stare back at us as if WE are the ones who do not know how to count?
I think we need to challenge our students more, not less.
ReplyDeleteSince 'challenge' is all we are after, I propose we have them move dirt around a yard, from pile to pile. CHALLENGE!
DeleteI am not really all that sympathetic to doing away with algebra.
ReplyDeleteBut if we are talking about reconfiguring math education it should start with *including statistics da*%it."
Statistics surround us every day, people don't know how to use them, understand them, and often make poor decisions because of misunderstood statistics. Just having one basic statistics class would make people much less susceptible to swallowing bogus statistics whole.
Only statisticians really understand statistics. Others may understand how to use them if they're lucky. And you don't need to take a class to understand that stats are manipulated to prove a point.
DeleteI have no problem with requiring 3 years of math - but at our local high school there is nothing except algebras, calculus, geometery, etc. Our students need a basic consumer math course that teaches them how to balance a check book, compound interest, what a discount of 30% actually means, how to compare prices of things. Inf act, perhaps they need 4 years with that being the foundation year. Or make that required senior year before they go out on their own.
ReplyDeleteI agree wholeheartedly. Why is personal finance not taught in high school? It's a necessary skill set.
Deletere: personal finance - I want the kids to learn that deception is the main tool of marketing = If you need it, you'll find it but advertising exists to decieve you into thinking you need something you don't. That money is power and that most businesses exist to transfer your power to someone else.
DeleteMy 80's Los Angeles Unified School Distric high school economics class instructed me on many facets of personal finance. I took notes and put them immediately into practice after graduating. But one of the things I learned almost crippled me financially:
"Claim exempt on your paycheck and put aside that money yourself. That way you earn intrest on the money before handing it over to Uncle Sam 'at the end of the year' AND anything left over can be moved to a higher yield/ risk investment."
It took me 4 years to pay the fines from the I.R.S. Apparently, they at least require quarterly payments. The penalty / bill was sent to my parent's address so I missed deadlines and things compounded from there... 'But my teacher said' is a poor defense.
As a high school teacher. I was always advocating for a class I would have called Life 101. It would cover the basics of necessary math--check books, budgeting, and doing at least the short form 1040. It would include basic nutrition, simple repairs from sewing on a button to plunging the toilet. Students would fill out job applications, provide references and have mock job interviews. I loved Algebra, geometry, trig, etc., but have used them rarely. The other skills are essential.
DeleteI totally agree, Barbwire.
DeleteYears ago I read somewhere a story about a high school that tried to offer a traditionally-girls' "homemaking" or "home economics" course to boys and met with resistance. They then renamed it "bachelor living" and it was accepted.
I personally love that strenuous mathematics are required to enter more prestigious schools. In the workforce, many occasions require a dedication to learning tasks or skills that will only hold value for a limited time. Although the content of algebra or calculus may be used infrequently in "real life," the mental dexterity and commitment required to learn a less-than-intriguing subject are great takeaways.
ReplyDeleteHowever, many hours must often be spent studying in order to merely pass a subject that will never be used again. Whereas those hours could have been put to better use mastering another in which you have more aptitude.
DeleteI agree that a shifted focus on statistics and personal finances would be a good thing. For programmers and other computer types, learning formal logic and extra practice on working in different bases would be very useful.
ReplyDeleteOn the other hand, it's just gotten a lot easier to learn algebra: http://www.wired.com/geekdad/2012/06/dragonbox/all/
That is the coolest thing, Mel. Thanks for sharing that.
DeleteAnd I think logic should be taught to every student everywhere.
Yeah the problem is that algebra is too hard, it has nothing to do with the failing standard of education. It's not even been a decade yet since I graduated high school. In sixth grade the average reading level that of a second or third grader. I read so fast they thought I was special needs. A few years ago I had explain slavery, the civil war, and civil rights to my fourteen year old cousin so she could understand the book she was reading for English class. One of the first classes I took at college was to me nothing more than refresher on high school math, but there were several people that struggled and a few that dropped because they lacked the basic math skills. And most of those had an attitude that they should get an 'A' just for showing up. Its not that Algebra is too hard its that up to that point education has failed to instill a good foundation of basics.
ReplyDeleteWhile Algebra can be challenging for many who aren't really math inclined, I too think it's also a problem of students not being taught to think. Critical thinking skills, logic and systematic problem solving are sorely lacking, and algebra relies on those fundamental skills... a problem with complex solutions, it is just another education stumbling block that Americans wish erroneously to isolate in order to fix it seems to me...
ReplyDeleteI use algebra every week. Calculus and mathematics that start getting into "imaginary" numbers and start to reside soley in theory... then maybe you can talk about not requiring an art genius to know.
ReplyDeleteThere are three possible explanations here: These children are not trying hard enough to learn these skills, the course is not being taught effectively, or young people today are simply not capable of learning these basic necessity maths like algebra, it's literally impossible.
I would gather to say the first 2 reasons are the primary problem for 90% of students.
My vote is that your reason number two feeds your reason number one.
DeleteWhen I started getting in trouble in junior high, I asked why I had to take harder classes (a.p.) than most of my friends, my guidance counselor told me, 'You are being taught Algebra to test how well you can follow instructions. When you graduate and are looking for a good college, your diploma is proof that you will do what you are told'.
This was the exact wrong thing to say to a 12 year old boy who was being denied time with his friends until his homework was completed.
Some research suggests that math deficits are found in children with mental health issues. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3046024/
ReplyDeleteI know that buried in some of my educational materials is a study that showed one could identify which teens had depression, etc based on their math grades.
The problem is, so many career fields are closed to those who cannot grasp the basics of math. I've taught children and those who are are classified with ED can often face great struggles with basic concepts of pre-algebra.
The mental health status of a child who is failing math should be taken into account.
If Bob is twice as old as Sally, and Sally is three times older than Sam, how many times older than Sam is Bob?
ReplyDeleteDo you really want someone diagnosing your pancreatitis who can't figure that out?
9 out of 10 doctors are just guessing anyway. That's why doctors call it 'practice'.
DeleteOf course, if you are going to dilute anesthesia for maximum gain and not get caught - you had better have some math skills!
Speaking as someone not educated in America, all I can say is "well, duh". _Of course_ someone not planning a career in which algebra is a job requirement should not be expected to study it at 10th grade level or later. Why are we even talking about this?
ReplyDelete(Sad to see that commenter Bub has gone for the strawman approach.)
Very few jobs require algebra. Very few jobs require you to do a sit-up, or drive around the orange cones, or read any book above a 5th-grade level, or criticize the motives of a fictional character. All of these activities teach the kind of thinking necessary to pick up whatever specific skills you need for your job and life. In the case of algebra, I believe the ability to manipulate arbitrary symbols and apply concrete rules to abstractions is a necessary one for most complex fields. It's a side issue whether the requirement serves as instruction or winnowing.
ReplyDeleteI'm not sure why that's a straw man - if you can't figure out simple algebra, you can't be a doctor, lawyer, accountant, engineer, et cetera and I don't consider that to be some sort of injustice. You can be a carpenter, but your career will be limited unless you are very very skilled to make up for it.
DeleteI'm pretty sure requiring math is winnowing for the most part, though engineers use algebra quite a bit. We're also required to take calculus. I've used calculus twice in a 30 year career.
My biggest problem is with HOW I was taught math. (grades not correct here; just for example)
ReplyDelete1st grade
You have two 2s, this is 2+2 and that is 4 ok.
3rd grade
Stop adding, we write that as 2X2=4 ok.
5th grade
Stop using X, use * instead ok.
7th grade
And instead of 2, use N so N*N=4 ok.
9th grade
Stop using *, use ( ) instead, so (N)(N)=4 ok.
Or hey, you don't HAVE to use the ( ) in this case, you can write N2 = 4 ok.
or N to the second power (which I cannot express here as superscript 2)= 4 ok.
Why was this changed so many times? While my brain may have benifited from these language/conception/interpretation shifts, I think it was an impediment to the speed of how much new math was learned.
Also, more than one of my teachers taught straight from the book. Looking back, I don't think they understood what they were teaching any better than I did - all lessons and tests were straight from the book.
While I do not think math is critical for everyone, art and science are closely coupled. If I did not have 'higher' math exposure in high school, I would not be the software programmer or the musician that I am today. (FWIW, I skipped college).
Supplemental.
DeleteHad N been brought in earlier, even adding and subtracting would have been easier because it would have eliminated that infuriating plus minus syntax.
2+2 =4 ok.
and 2 + -2 = 0 what?
N-2 = 0 ok.
cheers
I was fortunate to have been exposed to most math concepts before I entered school. One of my babysitters showed me addition, subtraction, division, and multiplication at the ripe old age of FOUR. Of course I did not understand all of these concepts at the time, but the very bare framework was there.
DeleteThis led to some frustrating times at school, though. In fourth grade they are teaching subtraction and tell me it's impossible to subtract a larger number from a smaller number, don't do it. I'm thinking in my head that there was some mechanism to cope with this, but oh well the teacher tells me it's impossible... I'll accept (with reservation noted). Fifth grade comes around and one of the first things we cover is negative numbers. WHAT... THE... Why lie to me as a kid? Tell me there is something called negative numbers and we are not going to cover it in the class, yet. Don't stunt my developing brain (that had already been opened 5 years earlier).
And by the way, 5th grade is when I really hit my stride. The bare framework was now filled with the rules and nuances of these mathematical manipulations. I finished just about every single test first in the class.
Another fluff piece from a parasitic journalism major who couldn't cut it in math or science.
ReplyDeleteAgreed.
DeleteActually, he's an emeritus political science professor from Princeton. He's usually very well-respected, but this one piece is making a very large percentage of those in scientific and mathematical fields very angry.
Deletehttp://qcpages.qc.cuny.edu/political_science/hacker.html
It enrages me that this debate about the usefulness of math keeps coming up. As long as we live in a capitalist society and base our economy on money, people need to understand how you can manipulate numbers. You can't go to the supermarket these days without doing math. My supermarket is full of signs saying that a some product is 3/$5. Or worse 7/$4. Now, most people can figure this stuff out. However, most people are utterly unaware of the difference between a product being half off, and getting half more for free. It is not the same people. And that's just in the supermarket.
ReplyDeleteWe're in a massive economic crisis now because a lot of people got loans they did not understand. You need proper algebra to understand such contracts.
We're going into an age of massively poor elderly, because a lot of people do not understand how their 401k works. Or how compounded interest works.
Furthermore, we are bombarded with statistic every day in the media. Statistics can misrepresent things enormously. An informed citizen needs to understand how statistics works, and unfortunately, statistics comes after algebra in math.
Finally, math, and especially algebra is enormously important to help children develop their abstract thinking.
It makes me desperate when people say you don't need math. You might as well say you don't need to be able to read. Everything is expressed in icons anyway.
I agree with you, so much, Nepkarel. Also, with the people who say they use algebra everyday. Even Mr. Professor Emeritus Author uses it, even though he doesn't realize it! Geometry and calculus principles too... and more!
DeleteSince when is anything in high school useful for a real worlld job? History? English literature/poetry? French? Marching Band? PE? Come on!
ReplyDeleteAnyone that has actually taken a decent Calculus class would realize this is when math becomes useful (and not just for math sake, but fundamental understanding of physical laws of nature), and algebra is just baby steps to that end.
I took one year of typing in high school - use it every day.
DeleteAgree with Bub re typing; it was the single most practical learning experience I had in either high school or college.
DeleteMe too (re typing class in high school)
DeleteThe classes that gave me the most often used _Practical_ knowledge were Shop and Agriculture. I had exceptional teachers for both, and they weren't the warehouse classes at our school as they so often are in others. Our teachers were a professional cabinet maker for shop and a man that held two PHD's in Ag. I learned to identify board by wood species, every freaking tool, fastener, type of measuring tool and style of measurement, mechanical drawing, joinery, roofing, plumbing and electrical parts and how to utilize them, all with hands-on class projects in addition to our individual projects. Did we use algebra in shop class? Oh hell yes! Try figuring the pitch of rafters for a school outbuilding without it. (yes, we Shop and Ag kids were used as free labor to build school and civic projects)
ReplyDeleteIn Ag, not only did I learn traditional things like how to identify and judge livestock, hay, etc., but we learned metalwork, small engine repair, and welding. Do you use algebra (and geometry) in Ag. You bet. Try figuring how much concrete to mix up to fill a posthole without it! Volume of a cylinder (hole) minus the volume of a cylinder (post) to solve for x (#bags of Quickcrete)? Both classes required the student to use tons of math. Thanks to two great teachers who showed this girl the practical side of that damn math that drove me so crazy in the classroom.
Oh, I forgot to add, the knowledge from these classes enabled me, among other things, to actually PASS Algebra and Geometry due to common sense, practical examples of why I needed it, and now, 20 years later to build my own home - to code. I can deal knowledgeably with plumbers, electricians, HV/AC techs, mechanics, etc. without getting taken to the cleaners too. I can replace light switches and outlets, install ceiling fans, or figure how much lumber needed for a project thanks to two men who refused to be an "Easy A" teachers.
DeleteYou go girl!
DeleteIn college, my professor, Dr. Rocky Ross told this story: He was going to teach his first computational theory class to masters students, and he asked an older professor what he should teach. The professor replied, "Rocky, it doesn't matter what you teach as long as it is hard."
ReplyDeleteOne of my favorite quotations is the following:
For your own purposes, and for the sake of Petronilla, which is really the same thing, consider the consequences of adopting, as an understanding of education, the ability to tell rubbish from Reason. Nothing more. Nothing but the power, and the propensity, to discover that a statement is worthless, or a term without meaning, or a proposition absurd. That would also be the power to make statements that are not worthless, and propositions that make demonstrable sense. That seems little enough to ask, although a moment's reflection will suggest that it is far more than it looks, and perhaps far more than we can imagine. But consider also the alternative of your adoption of such an understanding of education. Would you be willing to hold, as it seems to me that our general understanding of education does in fact hold, that the condition called "education" does not require the ability to tell rubbish from Reason, but only some powers by which to get along in the world?
Richard Mitchell's The Gift of Fire Chapter 9 ( http://www.sourcetext.com/grammarian/gift-of-fire/09.htm )
I have no objections to replacing algebra with some other mathematics, as long as it is hard and has right and wrong answers. I disagree however with replacing it with something merely to make it easier to pass school.
"If Bob is twice as old as Sally, and Sally is three times older than Sam, how many times older than Sam is Bob? Do you really want someone diagnosing your pancreatitis who can't figure that out?"
ReplyDeleteYes. I'd rather that he or she focus on my pancreas, thank you.
And when they have to figure out milligrams of an active agent based on your body weight and metabolic rate they can just screw up that unimportant part... your medication.
DeleteI'm sorry, did an artist steal your sense of humor? Or perhaps you were bullied by the drama club? :-P
DeleteThat Anonymous is me. Not sure why it didn't say that...
Deleteoh good grief. A life that never requires algebraic functions to be applied really isn't a life worth living.
ReplyDeleteI use it frequently to figure out volumes of supplies required for projects to beautify and enhance my surroundings, to calculate recipe adjustments for more delicious meals, to reverse engineer systems...and that's just personal use. At work I use it to calculate dilutions, purchase supplies, adjust experiments...I turn to algebra as an efficient means to many ends.
All that, and a great way to develop abstract thinking and problem solving in any arena. And as mentioned, a great way to determine the ability of others to do those things, as (for me) a way to assess relative intelligence, because frankly, if you can't think in the abstract at all, I will have difficulty finding common ground.
I would rather have a firm foundation of arithmetic and personal finance as the standard. I don't need quadratic equations or differential analysis to figure out recipes or interest rates. Algebra, as a subset of math, is more theoretical than practical for me.
ReplyDeleteAnd if I want to know how old Bob is, I'll ask him.
The trouble is partly caused by pretending that questions about how old Bob is are what elementary algebra is all about, which actually does more to suggest that abstract thinking ain't your cup of tea. Who said they needed quadratics for recipes or interest rates?
ReplyDeleteThat you know how to figure out what arithmetic to use is probably down to some basic algebraic juggling of the situation using variables and structure that has become practiced and not consciously accessed. The minute you introduce an "unknown" to an equation, you are doing elementary algebra. Why is that so unsettling?